Nonlinear and Adaptive Control Design for a Class of Flywheel Inverted Pendulum Systems

[[abstract]]本文針對特定類型之飛輪式倒單擺系統的平衡目的，提出了非線性遞迴步階和適應性控制設計方法。對於飛輪式倒單擺系統的一般情況，他是一個支點連接到擺錘，擺錘上的反動輪由輸入電壓驅動。飛輪式倒單擺系統的主要控制目標是將擺錘從任何初始點都能夠保持在垂直直立位置。 最初，分析和研究了簡單的線性化系統。此外，根據線性化系統設計得到的信息，可以應用在非線性系統的非線性遞迴步階控制器，以便對非線性飛輪式倒單擺進行模擬，實現平衡目的。下一步，考慮系統未知摩擦力的問題。採用適應性遞迴步階控制來克服摩擦力那未知且難以測量的問題。接下來，可以使用一些模擬結果來驗證所提出的控制器是否可以實現平衡控制目標。 此外，飛輪倒立擺系統的結果可以應用於特殊的Cubli系統，一個立方體可以利用剎車系統使其跳起在一個角落或邊緣上平衡。擺角限制在45度範圍內，因為它是在一個平台上運行。這裡我們主要討論一維模型。最後可以看出，所提出具有煞車系統的非線性和適應性步階控制器可以成功地實現讓Cubli跳起在邊緣上並平衡。[[abstract]]In this thesis, the nonlinear backstepping and adaptive control design schemes are developed for the balancing purpose of a class of flywheel inverted pendulum systems. For a general case of flywheel inverted pendulum, a fulcrum is used to be connected to pendulum and reaction wheel on the pendulum is driven by the input voltage. The main control objective of the flywheel inverted pendulum systems is to maintain the pendulum at the upright position from any initial point. In the beginning, the simpler linearized system is analyzed and investigated. Furthermore, according to the information obtained from the design of the linearized system, the nonlinear backstepping controller can be successfully developed to mani-pulate the nonlinear flywheel inverted pendulum to achieve balancing purpose. Next, the problem of the system's frictions is considered. Adaptive backstepping control is employed to overcome the problem that the frictional forces are unknown and difficult to measure. After all, some simulation results can be used to verify that the proposed controllers can achieve the balancing control objectives. Finally, the results of flywheel inverted pendulum can be applied to a special Cubli system, a cube can jump up and balance on a corner or edge. The pendulum angle is limited to be within ±45 degrees because it works on a platform. Here we mainly discuss the one-dimensional model. It can be shown that the proposed nonlinear backstepping controller with brake system can successfully achieve to let Cubli jump up and balance on an edge.[[note]]碩